Require
Export
Relations_1.
Require
Export
Relations_2.
Section
Relations_3.
Variable
U: Type.
Variable
R: (Relation U).
Definition
coherent : U -> U -> Prop :=
[x,y: U] (EXT z | (Rstar U R x z) /\ (Rstar U R y z)).
Definition
locally_confluent : U -> Prop :=
[x: U] (y,z: U) (R x y) -> (R x z) -> (coherent y z).
Definition
Locally_confluent : Prop := (x: U) (locally_confluent x).
Definition
confluent : U -> Prop :=
[x: U] (y,z: U) (Rstar U R x y) -> (Rstar U R x z) -> (coherent y z).
Definition
Confluent : Prop := (x: U) (confluent x).
Inductive
noetherian : U -> Prop :=
definition_of_noetherian:
(x: U) ((y: U) (R x y) -> (noetherian y)) -> (noetherian x).
Definition
Noetherian : Prop := (x: U) (noetherian x).
End
Relations_3.
Hints
Unfold coherent : sets v62.
Hints
Unfold locally_confluent : sets v62.
Hints
Unfold confluent : sets v62.
Hints
Unfold Confluent : sets v62.
Hints
Resolve definition_of_noetherian : sets v62.
Hints
Unfold Noetherian : sets v62.